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ISHIKAWA ITERATIVE PROCEDURE FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS 被引量:3
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作者 Zeng LuchuanDept. of Math., Shanghai Normal Univ.,Shanghai 200234. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第3期283-286,共4页
It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper pro... It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence. 展开更多
关键词 fixed point arbitrary Banach space Lipschitzian strictly pseudocontractive mapping ishikawa iterative procedure
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CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES 被引量:3
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作者 TIAN You-xian(田有先) +1 位作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1001-1008,共8页
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding r... Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces. 展开更多
关键词 convex metric space fixed point generalized ishikawa (Mann) iterative sequence with errors general quasi-contractive mapping
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ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS 被引量:1
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第1期3-14,共12页
The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The resul... The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results. 展开更多
关键词 Φ-pseudo contractive type mapping accretive mapping pseudo_contractive mapping Φ_strongly accretive mapping Φ_hemi_contractive mapping ishikawa iterative processes with error Mann iterative process with error
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CONVERGENCE RATE ESTIMATE OF ISHIKAWA ITERATIVE SEQUENCE FOR STRICTLY PSEUDOCONTRACTIVE MAPPINGS 被引量:1
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作者 Zeng LuchuanDept.ofMath.,ShanghaiNormalUniv.,Shanghai200234,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第2期189-192,共4页
Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in th... Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in this paper provides a convergence rate estimate. Moreover the resultin this paper improves,generalizes and summarizes some important and el- egant recent results 展开更多
关键词 arbitrary Banach space Lipschitzian mapping strictly pseudocontractive mapping fixed POINTS ishikawa iterative procedure
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MANN AND ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS FOR m-ACCRETIVE OPERATOR EQUATIONS 被引量:1
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第12期1310-1318,共9页
The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors... The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors' recent results. 展开更多
关键词 m _accretive operator Mann iterative sequence ishikawa iterative sequence
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ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES 被引量:2
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作者 曾六川 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第1期25-33,共9页
In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iter... In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461). 展开更多
关键词 φ-strongly accretive operator φ-hemicontractive operator ishikawa type iterative sequences with errors
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ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS
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作者 ZENG Liu-chuan(曾六川) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第6期686-693,共8页
The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschi... The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established. 展开更多
关键词 m-accretive operator ishikawa iterative sequence uniformly smooth Banach space
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ISHIKAWA ITERATIVE PROCESS IN UNIFORMLY SMOOTH BANACH SPACES
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作者 HUANG Zhen-yu(黄震宇) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第11期1306-1310,共5页
Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical meth... Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results. 展开更多
关键词 ishikawa iterative process Phi-stongly pseudocontractive operators uniformly smooth Banach spaces
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REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES
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作者 XUE Zhi-qun(薛志群) +1 位作者 TIAN Hong(田虹) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第12期1472-1476,共5页
The stability of the Ishikawa iteration procedures was studied for one class of continuity strong pseudocontraction and continuity strongly accretive operators with bounded range in real uniformly smooth Banach space.... The stability of the Ishikawa iteration procedures was studied for one class of continuity strong pseudocontraction and continuity strongly accretive operators with bounded range in real uniformly smooth Banach space. Under parameters satisfying certain conditions, the convergence of iterative sequences was proved. The results improve and extend the recent corresponding results, and supply the basis of theory for further discussing convergence of iteration procedures with errors. 展开更多
关键词 ishikawa iteration strongly pseudo-contractive operator uniformly smooth Banach space almost T-stable
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ON CONVERGENCE OF ISHIKAWA ITERATION PROCEDURES WITH ERRORS
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作者 叶新涛 倪仁兴 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2001年第1期105-120,共16页
The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbit... The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbitrary Banach spaces. As the direct applications, some stability results of the Ishikawa iteration methods for φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type are also given. Our results in this paper improve and extend the recent results due to Osilike and other authors. 展开更多
关键词 ON CONVERGENCE OF ishikawa ITERATION PROCEDURES WITH ERRORS
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Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping
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作者 张国伟 《Northeastern Mathematical Journal》 CSCD 2003年第2期174-180,共7页
Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique s... Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160). 展开更多
关键词 Mann and ishikawa iteration Φ-strongly accretive mapping conver-gence theorem
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ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS 被引量:8
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作者 Zeng LuchuanDept. of Math.,Shanghai Normal Univ.,Shanghai 200234. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第4期402-408,共7页
Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpans... Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions. 展开更多
关键词 Fixed point (asymptotically)nonexpansive mapping modified ishikawa iteration process Frechet differentiable norm Opial condition.
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ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED OINTS FOR ASYMPTOTICALLY NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES 被引量:7
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第1期25-34,共10页
Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained.
关键词 asymptotically nonexpansive mapping fixed point modified ishikawa iterative sequence with errors modified Mann iterative sequence with errors
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CONVERGENT PROBLEM OF ITERATIVE SEQUENCES FOR NONLINEAR MAPPINGS WITH ERROR MEMBERS IN BANACH SPACES 被引量:5
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作者 SunZhaohong NiYongqin HeChang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期81-89,共9页
In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are inv... In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results. 展开更多
关键词 asymptotically nonexpansive mapping asymptotically pseudocontractive mapping modified ishikawa iterative sequence with errors arbitrary Banach space fixed point.
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Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces 被引量:7
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作者 谷峰 《Northeastern Mathematical Journal》 CSCD 2001年第3期340-346,共7页
In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which exten... In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently. 展开更多
关键词 φ-pseudo contractive type mapping φ-hemi contractive type mapping strictly pseudo contractive mapping ishikawa iterative processes with error
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ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES 被引量:1
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作者 周海云 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期282-289,共8页
Let X be a real Banach space with a uniformly convex dual X*. Let T: X a X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L greater than or equal to 1 and a strongly accretive constant k... Let X be a real Banach space with a uniformly convex dual X*. Let T: X a X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L greater than or equal to 1 and a strongly accretive constant k epsilon (0,1). Let {alpha(n)} and {beta(n)} be two real sequences in [0,1] satisfying: (i) alpha(n) --> 0 as n --> infinity (ii) beta(n) < k(1 - k)/L(1 + L), for all n greater than or equal to 0; (iii) Pi(infinity) alpha(n) = infinity Set Sx = f - Tx + x, For All x epsilon X. Assume that {u(n)}(n=0)(infinity) and {v(n)}(n=0)(infinity) be two sequences in X satisfying parallel to u(n) parallel to = o(alpha(n)) and nu(n) --> 0 as n --> infinity. For arbitrary x(0) epsilon X, the iteration sequence {x(n)} is defined by (IS)(I) {x(n+1) = (1 - alpha(n))x(n) + alpha(n)Sy(n) + u(n), {y(n) = (1 - beta(n)) x(n) + beta(n)Sx(n) + v(n) (n greater than or equal to 0) then {x(n)} converges strongly to the unique solution of the equation Tx = f. related result deals with iterative approximation of fixed points of phi-hemicontractive mappings. 展开更多
关键词 ishikawa iteration with errors strongly accretive mapping phi-hemicontractive mapping
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A Note on Iterative Solutions of Nonlinear Accretive Operator Equations 被引量:1
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作者 张国伟 《Northeastern Mathematical Journal》 CSCD 2000年第4期459-462,共4页
Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process... Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers. 展开更多
关键词 ishikawa iteration strongly accretive operator Lipschitz operator
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SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES
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作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第4期394-408,共15页
Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, ... Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results. 展开更多
关键词 accretive mapping pseudo-contractive mapping hemi-accretive mapping hemi-pseudo-contractive mapping ishikawa iterative sequence Mann iterative sequence steepest descent sequence
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ITERATIVE PROCESS TO -HEMICONTRACTIVE OPERATOR AND-STRONGLY ACCRETIVE OPERATOR EQUATIONS
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作者 丁协平 张红琳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第11期1256-1263,共8页
Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n b... Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n be sequences in [0,1] satisfying:ⅰ) a n+b n+c n=a ′ n+b ′ n+c ′ n=1. n≥0; ⅱ) lim b n= lim b ′ n= lim c ′ n= 0; ⅲ)∑∞n=0b n=∞; ⅳ) c n=o(b n). For any given x 0,u 0,v 0∈K, define the Ishikawa type iterative sequence x n as follows: x n+1 =a nx n+b nTy n+c nu n, y n=a ′ nx n+b ′ nTx n+c ′ nv n (n≥0), where u n and v n are bounded sequences in K. Then x n converges strongly to the unique fixed point of T. Related result deals with the convergence of Ishikawa type iterative sequence to the solution of _strongly accretive operator equations. 展开更多
关键词 strongly accretive operator _hemicontrictive operator ishikawa type iterative sequence Banach space
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ITERATIVE PROCESS FOR CERTAIN NONLINEAR MAPPINGS WITH LIPSCHITZ CONDITION
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作者 GU Feng(谷峰) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第12期1458-1467,共10页
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive m... Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike. 展开更多
关键词 phi-strongly accretive operator phi-strongly pseudo-contractive mapping ishikawa iterative sequence Mann iterative sequence
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